Displaying faces in edit mode
Face dots are not displayed if Textured Solid is enabled in 3D View > N-panel > Shading.

Odd theme colors could make it hard to see the face dots, but that's not the reason in your case. Unselected faces use the wire color for both, the edges and the face dot, which is light purple in your screenshot (so clearly distinguishable from the surroundings).

As last resort, submit a bug report to the tracker.